Average Error: 0.5 → 0.5
Time: 2.6s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{x - 1} \cdot \sqrt{x}\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{x - 1} \cdot \sqrt{x}
double f(double x) {
        double r1179 = x;
        double r1180 = 1.0;
        double r1181 = r1179 - r1180;
        double r1182 = sqrt(r1181);
        double r1183 = sqrt(r1179);
        double r1184 = r1182 * r1183;
        return r1184;
}
↓
double f(double x) {
        double r1185 = x;
        double r1186 = 1.0;
        double r1187 = r1185 - r1186;
        double r1188 = sqrt(r1187);
        double r1189 = sqrt(r1185);
        double r1190 = r1188 * r1189;
        return r1190;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Final simplification0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))